<h2>Problem 240</h2>
<div style="color:#666;font-size:80%;">10 April 2009</div><br />
<div class="problem_content">
<p>There are 1111 ways in which five 6-sided dice (sides numbered 1 to 6) can be rolled so that the top three sum to 15. Some examples are:

<br /><br />
D<img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>3</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>4</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>5</sub><img src="" style="display:none;" alt=")" /> = 4,3,6,3,5
<br />
D<img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>3</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>4</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>5</sub><img src="" style="display:none;" alt=")" /> = 4,3,3,5,6
<br />
D<img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>3</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>4</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>5</sub><img src="" style="display:none;" alt=")" /> = 3,3,3,6,6
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D<img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>3</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>4</sub><img src="" style="display:none;" alt=")" />,D<img src="" style="display:none;" alt="_(" /><sub>5</sub><img src="" style="display:none;" alt=")" /> = 6,6,3,3,3
<br /><br />
In how many ways can twenty 12-sided dice (sides numbered 1 to 12) be rolled so that the top ten sum to 70?</p>
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